Amplifiers, ubiquitous building blocks in myriad applications, are at the simplest level characterized by two operational properties—bandwidth and gain—both of which are ideally large. In many standard designs based on resonant cavities or circuits, increasing either the gain or bandwidth necessarily comes with a sacrifice in the other quantity. It would however be highly desirable to obtain increased gain without unduly sacrificing the bandwidth. This naturally leads to extended structures (e.g. travelling wave amplifiers), whose large size makes them more susceptible to disorder and imperfections introduced during the fabrication of the amplifier. It is also desirable to have robust amplifiers that are minimally affected by such imperfections. Furthermore, in many sensitive applications, it would be desirable to have an amplifier be truly unidirectional, meaning that it strongly amplifies signals arriving from a source but prevent any transmission of signals or noise to the source (thus protecting a potentially fragile signal source). Amplifiers whose noise properties approach the fundamental limits set by quantum mechanics are also highly desirable in a variety of contexts, ranging from quantum information processing in circuits to radio astronomy and ultrasensitive force detection.